2,343 research outputs found
Analyzing the Effect of Objective Correlation on the Efficient Set of MNK-Landscapes
In multiobjective combinatorial optimization, there exists two main classes
of metaheuristics, based either on multiple aggregations, or on a dominance
relation. As in the single objective case, the structure of the search space
can explain the difficulty for multiobjective metaheuristics, and guide the
design of such methods. In this work we analyze the properties of
multiobjective combinatorial search spaces. In particular, we focus on the
features related the efficient set, and we pay a particular attention to the
correlation between objectives. Few benchmark takes such objective correlation
into account. Here, we define a general method to design multiobjective
problems with correlation. As an example, we extend the well-known
multiobjective NK-landscapes. By measuring different properties of the search
space, we show the importance of considering the objective correlation on the
design of metaheuristics.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome :
Italy (2011
On the Effect of Connectedness for Biobjective Multiple and Long Path Problems
Recently, the property of connectedness has been claimed to give a strong
motivation on the design of local search techniques for multiobjective
combinatorial optimization (MOCO). Indeed, when connectedness holds, a basic
Pareto local search, initialized with at least one non-dominated solution,
allows to identify the efficient set exhaustively. However, this becomes
quickly infeasible in practice as the number of efficient solutions typically
grows exponentially with the instance size. As a consequence, we generally have
to deal with a limited-size approximation, where a good sample set has to be
found. In this paper, we propose the biobjective multiple and long path
problems to show experimentally that, on the first problems, even if the
efficient set is connected, a local search may be outperformed by a simple
evolutionary algorithm in the sampling of the efficient set. At the opposite,
on the second problems, a local search algorithm may successfully approximate a
disconnected efficient set. Then, we argue that connectedness is not the single
property to study for the design of local search heuristics for MOCO. This work
opens new discussions on a proper definition of the multiobjective fitness
landscape.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome :
Italy (2011
Controlled non uniform random generation of decomposable structures
Consider a class of decomposable combinatorial structures, using different
types of atoms \Atoms = \{\At_1,\ldots ,\At_{|{\Atoms}|}\}. We address the
random generation of such structures with respect to a size and a targeted
distribution in of its \emph{distinguished} atoms. We consider two
variations on this problem. In the first alternative, the targeted distribution
is given by real numbers \TargFreq_1, \ldots, \TargFreq_k such that 0 <
\TargFreq_i < 1 for all and \TargFreq_1+\cdots+\TargFreq_k \leq 1. We
aim to generate random structures among the whole set of structures of a given
size , in such a way that the {\em expected} frequency of any distinguished
atom \At_i equals \TargFreq_i. We address this problem by weighting the
atoms with a -tuple \Weights of real-valued weights, inducing a weighted
distribution over the set of structures of size . We first adapt the
classical recursive random generation scheme into an algorithm taking
\bigO{n^{1+o(1)}+mn\log{n}} arithmetic operations to draw structures from
the \Weights-weighted distribution. Secondly, we address the analytical
computation of weights such that the targeted frequencies are achieved
asymptotically, i. e. for large values of . We derive systems of functional
equations whose resolution gives an explicit relationship between \Weights
and \TargFreq_1, \ldots, \TargFreq_k. Lastly, we give an algorithm in
\bigO{k n^4} for the inverse problem, {\it i.e.} computing the frequencies
associated with a given -tuple \Weights of weights, and an optimized
version in \bigO{k n^2} in the case of context-free languages. This allows
for a heuristic resolution of the weights/frequencies relationship suitable for
complex specifications. In the second alternative, the targeted distribution is
given by a natural numbers such that
where is the number of undistinguished atoms.
The structures must be generated uniformly among the set of structures of size
that contain {\em exactly} atoms \At_i (). We give
a \bigO{r^2\prod_{i=1}^k n_i^2 +m n k \log n} algorithm for generating
structures, which simplifies into a \bigO{r\prod_{i=1}^k n_i +m n} for
regular specifications
Experiments on local search for bi-objective unconstrained binary quadratic programming
International audienceThis article reports an experimental analysis on stochastic local search for approximating the Pareto set of bi-objective unconstrained binary quadratic programming problems. First, we investigate two scalarizing strategies that iteratively identify a high-quality solution for a sequence of sub-problems. Each sub-problem is based on a static or adaptive definition of weighted-sum aggregation coefficients, and is addressed by means of a state-of-the-art single-objective tabu search procedure. Next, we design a Pareto local search that iteratively improves a set of solutions based on a neighborhood structure and on the Pareto dominance relation. At last, we hybridize both classes of algorithms by combining a scalarizing and a Pareto local search in a sequential way. A comprehensive experimental analysis reveals the high performance of the proposed approaches, which substantially improve upon previous best-known solutions. Moreover, the obtained results show the superiority of the hybrid algorithm over non-hybrid ones in terms of solution quality, while requiring a competitive computational cost. In addition, a number of structural properties of the problem instances allow us to explain the main difficulties that the different classes of local search algorithms have to face
On a Cardinality Constrained Multicriteria Knapsack Problem
We consider a variant of a knapsack problem with a fixed cardinality constraint. There are three objective functions to be optimized: one real-valued and two integer-valued objectives. We show that this problem can be solved efficiently by a local search. The algorithm utilizes connectedness of a subset of feasible solutions and has optimal run-time
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